Abstract
A small fraction of the binary relativistic systems display the "black widow" effect: the companion is being ablated by the (recycled) pulsar wind. In these binary systems the evolution of the companion star (of the solar-type) reaches the point of filling its Roche lobe, thus initiating the process of mass accretion onto the pulsar. Accretion is generally believed to result in magnetic field decay, while isolated neutron star fields decay very slowly, if at all. We shall show that the very long evolution of the "black widow" system, starting from a solar-type star and lasting > 5 Gyr to reach the observed position in the plane, allows us to conclude that the magnetic field does not decay below the bottom value , extending the previous conclusions drawn from younger systems. In addition, the masses of the "black widow" pulsars are naturally predicted to be > 2 Mo due to the accretion history, in full agreement with recent measurements.
